The amplitude of the breathing motion depends on both \(Z\)  and \(R\) . The spiral density waves could drive alternate expanding and compressive motions along the Galactocentric radius near the plane ([1]}; [2]}; [3]}), and contribute to an increasing amplitude of breathing motions with distance to the plane within the range \(|Z|\lesssim 1\,\mathrm {kpc}\)  [3]}. However, considering that the observed \(|V_{\rm {breath}}|\)  increases with the vertical height towards \(|Z|\sim 3\,\mathrm {kpc}\) , it is unlikely that the breathing mode motion is totally attributed to spirals. As for the bending motion, [3]} argued that the spirals are probably not responsible for the bending mode. [6]} proposed that the bending-mode oscillation could be induced by a buckling bar inhabited in the disk. The differences in vertical bulk velocities between different \(\rm {[Fe/H]}\)  are trivial, indicating that different populations respond similarly to the perturbations. In this case, we infer that both the breathing and bending motions are produced or partly produced by long-lived external perturbations such as a satellite galaxy. It has been argued that the perturbed vertical motions could be generated by the Sagittarius dwarf-Milky Way interaction ([7]}; [8]}; [9]}; [10]}; [11]}).
